The response of a Bernoulli-Euler beam supported by a Winkler-type elastic foundation with inertia and subjected to a moving load is investigated. Steady-state solutions are determined for an undamped and linearly damped beam-foundation system. The effects on the response of load velocity, foundation mass, and damping are studied. For the undamped system, it is well known that the response grows without bound as a certain critical velocity is approached-. It is shown that the effect of foundation mass is to reduce the critical velocity and to increase the peak deflection. The increase in peak deflection becomes more pronounced as the critical velocity is approached. As in the case of massless foundation, the deflection wave is observed to be symmetric with respect to the load. When damping is introduced, the deflection wave loses its symmetry, and the peak deflection is reduced. Results for both cases are given in graphical form. NomenclatureA = beam cross-sectional area E = Young's modulus of beam material E f = Young's modulus of foundation / = moment of inertia of beam P = dimensionless concentrated traveling load Re = real part of a complex quantity U = dimensionless foundation displacement V = load dimensionless velocity W = dimensionless beam deflection W p = peak (dimensionless) beam deflection W s = peak static (dimensionless) beam deflection c = viscous damping coefficient for beam Cf = velocity of plane wave propagation in foundation, see Eq. (2) g n = constants, see Eqs. (21) h = beam width k f = spring modulus of foundation (force/unit area) m = beam density (mass per unit length) q -foundation pressure (F/L) r = radius of gyration of beam (V/A4) t = time u = foundation displacement v = load velocity w = beam deflection x = coordinate along beam axis y = variable in characteristic equation, see Eq. (19) z = coordinate normal to beam axis, see Eq. (2) ft = "bouncing frequency" of beam on massless foundation a. = ratio of foundation stiffness to beam stiffness (mr 4 Q 2 /EI) P 2 = ratio of the mass-per-unit length of the foundation to the mass-per-unit-length of the beam (pt/m) y = dimensionless distance along beam axis (£ -Vr) rj = dimensionless distance along foundation, positive down(z/r) 0 = dimensionless damping coefficient (c/2mtt) \ = separation constant for foundation equation, also variable in characteristic equation, see Eqs. (11), (17), and (18)